加权Schatten范数低秩表示的高光谱图像恢复

高光谱图像在获取过程中常受到多种噪声的干扰, 如高斯噪声、脉冲噪声、条纹噪声等, 为确保后续应用的顺利进行, 提出了一种基于加权Schatten范数低秩表示的高光谱图像恢复方法。该方法引入低秩表示模型恢复高光谱数据, 采用加权Schatten范数代替核函数, 更精确地逼近秩函数; 并选用初步无噪图像作为低秩表示的字典, 进一步提高了模型对图像的恢复能力。另外, 引入拉普拉斯正则项刻画数据内部的几何结构, 能保持图像的细节。模拟和实际高光谱数据的实验结果表明, 较多种相关的方法在视觉效果和量化指标值都有很大地改进。与经典的基于低秩先验的恢复方法相比, 本文算法的平均峰值信噪比提高2.74 dB, 平均结构相似性数值指标提高0.03, 而平均光谱角降低1.40。新模型不仅能充分利用高光谱图像光谱维的低秩先验, 而且保持了数据内部的几何结构, 有利于恢复出高质量的清晰图像。

Abstract

Hyperspectral Image (HSI) always suffers from various noises such as Gaussian noise, impulse, stripe noise, etc. To ensure the performance of subsequent applications, a new method for HSI restoration was proposed based on weighted Schatten norm Low-Rank Representation (LRR). The proposed method introduced the LRR model into the HSI restoration. It can accurately approximate rank using the weighted Schatten norm instead of the nuclear norm. Furthermore, the initial noiseless image was utilized as the dictionary for LRR to improve the restoration ability. Then, the Laplacian regularizer was used to describe the intrinsic geometric information of the data and to protect details of the HSI. Experimental results on synthetic and real HSI data demonstrated that the proposed method achieves better visual quality and quantitative indices than several existing related methods. Compared with the classical restoration method based on low-rank priori, the mean peak signal-to-noise ratio and structural similarity indices of this algorithm increased by 2.74 dB and 0.03 respectively, and the mean spectral angle was reduced by 1.40. The new method not only takes advantage of the low-rank prior information in the spatial domain, but also keeps the intrinsic geometric structures in data, which helps restore quality clean images.

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张倩颖, 谢晓振. 加权Schatten范数低秩表示的高光谱图像恢复[J]. 光学精密工程, 2019, 27(2): 421. ZHANG Qian-ying, XIE Xiao-zhen. Hyperspectral image restoration via weighted Schatten norm low-rank representation[J]. Optics and Precision Engineering, 2019, 27(2): 421.

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